CN110285970A - The rolling bearing Weak fault Enhancement Method restored based on matrix - Google Patents

The rolling bearing Weak fault Enhancement Method restored based on matrix Download PDF

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CN110285970A
CN110285970A CN201910647394.2A CN201910647394A CN110285970A CN 110285970 A CN110285970 A CN 110285970A CN 201910647394 A CN201910647394 A CN 201910647394A CN 110285970 A CN110285970 A CN 110285970A
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matrix
signal
fault
fault message
positive sequence
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CN110285970B (en
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马辉
俞昆
付强
曾劲
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Northeastern University China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G01M13/04—Bearings
    • G01M13/045—Acoustic or vibration analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing
    • G06F2218/04—Denoising

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  • Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • General Physics & Mathematics (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
  • Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)

Abstract

Based on the rolling bearing Weak fault Enhancement Method that matrix restores, belong to rotary machinery fault diagnosis technical field.By constructing fault message matrix, collected one-dimensional vibration signal is expressed as to the form of two dimensional fault information matrix, to meet the input requirements of matrix Renew theory, restore derivation algorithm using matrix and recovers the low-rank matrix comprising shock characteristic from two dimensional fault information matrix, on this basis, the vibration signal of removal noise jamming is recovered from low-rank matrix using cumulative mean algorithm.At the same time, consider that inevitably phenomenon is truncated in tail portion when construction fault message matrix, positive sequence, backward fault message matrix are constructed to positive sequence, backward vibration signal respectively, above three step is executed to two fault message matrixes respectively, and the denoising information obtained by above-mentioned two fault message matrix is synthesized to obtain final denoised signal.Characteristic of rotating machines vibration signal analysis etc. of this method suitable for rotary machinery fault diagnosis field.

Description

The rolling bearing Weak fault Enhancement Method restored based on matrix
Technical field
The invention belongs to rotary machinery fault diagnosis technical fields, and it is faint to be related to a kind of rolling bearing restored based on matrix Failure Enhancement Method.
Background technique
Matrix restores, and is proposed earliest by John Wright et al., also known as Robust PCA or sparse and low-rank matrix It decomposes, refers to after certain elements of matrix are seriously damaged, automatically identify the element of destruction, recover original matrix.Equally, It is assumed that original matrix has very good structure, it is low-rank；Further, it is assumed that only a small part element is seriously damaged, I.e. noise is sparse but size can be any.Then matrix recovery can be described with following optimization problem:
Wherein, objective function is the order of matrix L and zero norm of noise matrix S, the i.e. number of the nonzero element of S, λ table Weight shared by bright noise.Equally, this is a NP-Hard problem, without effective derivation algorithm.Thus it is possible to use matrix Nuclear norm approximation order, 1 norm of matrix carrys out approximate zero norm, and formula (1) is converted into following problem:
Wherein, L representing matrix, λ show weight shared by noise, and S indicates noise matrix, | | | | the l of * representing matrix1 Norm, D indicate observing matrix；
This is a convex optimization problem, and for such problem, there are many effective derivation algorithms at present.
Matrix recovery has been obtained extensively in field of image processing (such as: background modeling, batch alignment, image segmentation) Application.Illustrate that the application mode that matrix restores, the most simple case of background modeling are to take the photograph phase from fixation by taking background modeling as an example Separating background and prospect in the video of machine shooting.At this time it is readily conceivable that background is basically unchanged, so if background A column of each frame as matrix, then the matrix low-rank.Simultaneously because prospect is mobile object, it is lower to occupy pixel ratio, So prospect corresponds to sparse " noise " ingredient in video.Thus obtain doing the matrix Restoration model of background modeling, wherein D Each column are the vectors obtained after each frame of video is straightened, and each frame that each column of matrix L correspond to background obtains after being straightened The vector arrived, the vector that each frame that each column of matrix S correspond to prospect obtains after being straightened.It is similar therewith, work as rolling bearing When failure, since ball leads to contact force cyclically-varying by fault zone, so that being generated in vibration signal constant Equally spaced impact ingredient, the part may be considered low-rank, however, in bearing vibration signal collection process, unavoidably Ground will appear noise jamming, and due to ambient noise random distribution, which may be considered sparse " noise " ingredient.Rolling bearing When there is initial failure, ambient noise interference is larger, and effective impact ingredient in vibration signal is more faint, constructs bear vibration The matrix Restoration model of signal extracts because impacting ingredient caused by local fault, realizes the enhancing of bearing Weak fault feature.
Summary of the invention
Present invention seek to address that feel in the prior art the problem of, provide it is a kind of based on matrix restore rolling bearing it is micro- Weak failure Enhancement Method.
Technical solution of the present invention:
Based on the rolling bearing Weak fault Enhancement Method that matrix restores, fault message matrix construction, low-rank are specifically included that Matrix restores and impact signal restores three steps.Meanwhile in order to guarantee the enhanced failure letter of final weak impact feature Number length is consistent with original signal strength, vibration signal tail portion truncated problem caused by avoiding because of construction fault message matrix, Above three step is executed respectively to the vibration signal data of permutation with positive order and the vibration signal data reversed respectively, most Eventually by synthesizing to the impact signal recovered according to positive sequence, the vibration signal data reversed, weak impact is obtained The enhanced fault-signal of feature, by carrying out spectrum analysis, envelope spectrum point to the enhanced fault-signal of weak impact feature Analysis can be realized effectively and differentiate rolling bearing fault state.This patent mentions the rolling bearing Weak fault restored based on matrix Enhancement Method flow chart is as shown in Figure 1.
This patent is proposed the rolling bearing Weak fault Enhancement Method restored based on matrix and specifically executes that steps are as follows:
Step 1: assuming that collected vibration signal is d=[d1, d2..., dN], wherein N is that the sampling of vibration signal is long Degree constructs positive sequence fault message matrix D by vibration signal1Are as follows:
Wherein
F=floor (Fs/Fc), (4) and
In formula, n+f and k respectively indicate constructed positive sequence fault message matrix D1Columns and line number, FsTo be acquired vibration The sample frequency of dynamic signal, FcBy acquisition vibration signal fault characteristic frequency, n be setting extra time length,Table Show downward floor operation.Ideally, in positive sequence fault message matrix the serial number n+kf of lower right corner element should be less than or Equal to vibration signal sampling length N.
Step 2: by the positive sequence fault message matrix D of construction1It substitutes into matrix Restoration model shown in formula (2), utilizes square Battle array restores derivation algorithm, is low-rank matrix L by positive sequence fault message matrix-split1With noise matrix S1.Extracted low-rank matrix L1It is represented by following form:
Step 3: by low-rank matrix L1The form for being arranged in one-dimensional signal restores impact ingredient R1.In view of restoring through matrix There are difference for element numerical value in low-rank matrix that treated at same sequence number, handle low-rank in such a way that cumulative mean is handled Element in matrix at same sequence number, finally obtaining the denoised signal being made of n+kf element after restoring is R1=[r1, r2..., rn+kf]。
Below for restoring the 2f element, illustrate the specific steps of cumulative mean processing:
1. construction label matrix L abel[2f]The element d for being 2f for marking serial numbers2fIn positive sequence fault message matrix
D1The position of middle appearance:
Wherein 1≤i≤(k-1) f+1,1≤j≤n+f.What needs to be explained here is that label matrix L abel dimension with just Sequence fault-signal matrix D1Dimension it is identical.
2. according to label matrix L abel[2f]Calculate the element d that marking serial numbers are 2f2fIn positive sequence fault message matrix
D1The number of middle appearance:
num2f=sum (Label[2f]) (8)
3. calculating the numerical value of the element of 2f in the signal after restoring according to following formula:
r2f=sum < L1, Label[2f]>/num2f (9)
In formula,<,>indicate that two matrix elements carry out dot product.
Step 4: due to according to positive sequence fault message matrix D1It is only capable of effectively restoring to be gone by what preceding n+kf data point formed Noise cancellation signal, in order to ensure the denoised signal length finally restored is consistent with original signal, the vibration signal d=that acquired original is arrived [d1, d2..., dN] carry out backward processingUtilize the vibration signal of backwardConstruction Backward fault message matrix D2, it is shown below:
Step 5: to backward fault-signal matrix D2Step 2,3 shown operations are executed, to obtain low after matrix restores Order matrix L2And the backward denoised signal being made of n+kf element isBelieved by denoising backward It number is inverted and to obtain its corresponding positive sequence and be expressed asWherein p=N- (n+kf) +1.Utilize denoised signal R1And R2Synthesize final denoised signal R, expression formula are as follows:
Element in formula, in denoised signal RIt is calculated by following formula:
According to above-mentioned steps, final denoised signal R is obtained.By carrying out spectrum analysis and envelope spectrum to denoised signal R Analysis can determine whether the malfunction of rolling bearing.
Beneficial effects of the present invention: using the mentioned method of this patent can effectively remove in rolling bearing fault signal with therefore Hinder unrelated other frequency contents interference of characteristic frequency, it is greatly enlarged to draw shock characteristic caused by local fault, to reach event Hinder the purpose of feature enhancing.And the mentioned method of this patent has artificial setting parameter few, the high feature of computational efficiency.
Detailed description of the invention
Fig. 1 is the rolling bearing Weak fault Enhancement Method flow chart restored based on matrix.
Fig. 2 is noisy acoustic simulation signal, wherein (a) is time domain waveform, (b) is frequency-domain waveform, (c) is envelope spectrum.
Fig. 3 denoises post-simulation signal to be proposed method using this patent, wherein (a) is time domain waveform, (b) is frequency domain wave Shape (c) is envelope spectrum.
Fig. 4 is to denoise post-simulation signal using spectrum kurtosis technology, wherein (a) is spectrum kurtosis figure, (b) is time-domain signal, It (c) is envelope spectrum.
Fig. 5 is outer ring malfunction test signal, wherein (a) is time domain waveform, (b) is frequency-domain waveform, (c) is envelope spectrum.
Fig. 6 is is mentioned experimental signal after method denoises using this patent, wherein (a) is time domain waveform, (b) is frequency domain wave Shape (c) is envelope spectrum.
Fig. 7 is to utilize experimental signal after spectrum kurtosis technology denoising, wherein (a) is spectrum kurtosis figure, (b) is time-domain signal, It (c) is envelope spectrum.
Specific embodiment
The present embodiment proves the validity of the proposed method of this patent by setting emulation case, experiment case study.
1. emulating case
It emulates in case, signal is emulated by following formula construction bearing fault:
In formula: Am=0.9 maximum amplitude impacted for m-th, β1=380 be damping coefficient, ωn1=2048Hz is It is assumed that bearing fault frequency, TbThe time interval between adjacent two punching is indicated, caused by δ T is indicated because of sliding when adjacent two impacts Between the error that is spaced, value is 1~2%Tb, μ (t) is unit switch function.Assuming that bearing outer ring breaks down, failure-frequency For 125Hz, signal sampling frequencies 20kHz, sampling time 1s.By be added signal-to-noise ratio be -17db white Gaussian noise come Simulation background noise jamming, the emulation time domain plethysmographic signal constructed are as shown in Figure 2 with its frequency spectrum, envelope spectrum.It observes in Fig. 2 (c) it is found that being difficult to observe obvious peak value at failure-frequency and its frequency multiplication, bearing fault characteristics are very faint.
Signal shown in (a) in Fig. 2 is handled using the mentioned Weak fault Enhancement Method of this patent, obtains denoised signal as schemed Shown in (a) in 3, and (b), (c) in diagnostic result such as Fig. 3 are obtained to denoised signal progress spectrum analysis, envelope spectrum analysis It is shown.Observation it is found that be remarkably reinforced using the shock characteristic in the mentioned Weak fault Enhancement Method of this patent treated signal, There are obvious peak values at failure-frequency and its frequency multiplication in its envelope spectrum, can effectively judge rolling bearing fault state.
In order to further illustrate the validity of mentioned method herein, gives and utilize the diagnosis knot after spectrum kurtosis technical treatment Fruit is as shown in Figure 4.There it can be seen that shock characteristic is not obvious enough in treated time-domain signal, failure frequency in envelope spectrum Do not occur apparent peak value at rate and its frequency multiplication, traditional spectrum kurtosis technology cannot be effectively treated such ambient noise interference compared with Strong bearing fault signal.
2. experiment case study
By taking the N205EM type housing washer fault-signal of actual acquisition as an example, the effective of the mentioned method of this patent is verified Property.
It acquires shown in (a) in the outer ring fault-signal such as Fig. 5 when revolving speed is 8Hz, by carrying out spectrum analysis, packet to it Network spectrum analysis result such as (b) in Fig. 5, shown in (c) in 5.(c) in Fig. 5 is observed it is found that since revolving speed is lower, experiment is adopted It is interfered during collection by stronger turn of frequency, leads to amplitude Relative fault frequency at envelope spectrum transfer frequency and its frequency multiplication and its again Amplitude at frequency is significantly greater.
In order to effectively remove the interference of unrelated frequencies ingredient, protrusion is drawn the impact ingredient that failure obtains, is mentioned using this patent Shown in (a) in denoised signal Fig. 6 that method is handled, spectrum analysis is carried out to it, result that envelope spectrum analysis obtains such as Shown in (c) in (b), Fig. 5 in Fig. 6.Observation it is found that the mentioned method of this patent can effectively remove unrelated frequencies ingredient do It disturbs, the amplitude in envelope spectrum at failure-frequency and its frequency multiplication is more prominent.
As a comparison, it gives as shown in Figure 7 using the result of the spectrum kurtosis technical treatment experimental signal.Turn frequency due to drawing Caused time-domain signal peak value is opposite, and to draw impact peak value caused by local fault larger, composes kurtosis to the biggish component of amplitude more Sensitivity, thus in the time-domain signal extracted using spectrum kurtosis the two peak-to-peak intervals of protrusion with to turn frequency consistent, envelope spectrum transfer frequency compared with It is obvious.Spectrum kurtosis technology cannot handle such experimental signal well.

Claims (2)

1. the rolling bearing Weak fault Enhancement Method restored based on matrix, which is characterized in that steps are as follows:
Step 1: setting collected vibration signal as d=[d1, d2..., dN], wherein N is the sampling length of vibration signal, by shaking Dynamic signal constructs positive sequence fault message matrix D1Are as follows:
Wherein
And
In formula, n+f and k respectively indicate constructed positive sequence fault message matrix D1Columns and line number, FsTo be acquired vibration letter Number sample frequency, FcBy acquisition vibration signal fault characteristic frequency, n be setting extra time length,Indicate to Lower floor operation；Ideally, the serial number n+kf of lower right corner element should be less than or equal in positive sequence fault message matrix Vibration signal sampling length N；
Step 2: by the positive sequence fault message matrix D of construction1It substitutes into matrix Restoration model shown in formula (2):
Wherein, L indicates low-rank matrix, and λ > 0 shows that regularization coefficient, S indicate noise matrix, | | | |*The core model of representing matrix Number, | | | |1The l of representing matrix1Norm, D indicate observing matrix；
Restore derivation algorithm using matrix, is low-rank matrix L by positive sequence fault message matrix-split1With noise matrix S1；It is extracted Low-rank matrix L1It is expressed as form:
Step 3: by low-rank matrix L1The form for being arranged in one-dimensional signal restores impact ingredient R1；In view of being handled through matrix recovery There are difference for element numerical value in low-rank matrix afterwards at same sequence number, handle low-rank matrix in such a way that cumulative mean is handled Element at middle same sequence number, finally obtaining the denoised signal being made of n+kf element after restoring is R1=[r1, r2..., rn+kf]；Step 4: according to positive sequence fault message matrix D1It is only capable of the denoised signal for effectively restoring to be made of preceding n+kf data point, In order to ensure the denoised signal length finally restored is consistent with original signal, vibration signal d=[d that acquired original is arrived1, d2..., dN] carry out backward processingUtilize the vibration signal of backwardIt constructs inverse Sequence fault message matrix D2, it is shown below:
Step 5: to backward fault-signal matrix D2Operation shown in step 2, step 3 is repeated, thus after obtaining matrix recovery Low-rank matrix L2And the backward denoised signal being made of n+kf element isBy the way that backward is gone Noise cancellation signal, which is inverted to obtain its corresponding positive sequence, to be expressed asWherein p=N- (n +kf)+1；Utilize denoised signal R1And R2Synthesize final denoised signal R, expression formula are as follows:
Element in formula, in denoised signal RIt is calculated by following formula:
The malfunction of rolling bearing just can be judged by carrying out spectrum analysis and envelope spectrum analysis to denoised signal R.
2. the rolling bearing Weak fault Enhancement Method according to claim 1 restored based on matrix, which is characterized in that step The specific steps that cumulative mean is handled in rapid 3:
When restoring 2f element:
(3.1) construction label matrix L abel[2f]The element d for being 2f for marking serial numbers2fIn positive sequence fault message matrix D1In go out Existing position:
Wherein 1≤i≤(k-1) f+1,1≤j≤n+f；Mark the dimension and positive sequence fault-signal matrix D of matrix L abel1Dimension It is identical；
(3.2) according to label matrix L abel[2f]Calculate the element d that marking serial numbers are 2f2fIn positive sequence fault message matrix D1In go out Existing number:
num2f=sum (Label[2f]) (8)
(3.3) numerical value of the element of 2f in the signal after restoring is calculated according to following formula:
r2f=sum < L1, Label[2f]>/num2f (9)
In formula,<,>indicate that two matrix elements carry out dot product.
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